The Hazards of Applying Hazard Ratios to Accelerated Failure Time Models: A Simulation Study

OBJECTIVES: In Health Technology Assessment (HTA) indirect comparisons are often required when head-to-head data is unavailable. In these instances, a survival model is often fitted to one treatment, and then hazard ratios (HR) from an indirect comparison are applied to produce survival curves for the comparators. Common survival models use proportional hazards (PH) or accelerated failure time (AFT) frameworks. Best practice would suggest that the treatment effect should be applied to a model that uses the same scale, such as applying an HR to a PH survival model. However, in HTA, it is common for HRs to be applied to AFT models. This study explores the impact of this sub-optimal practice.

METHODS: We simulated survival data for two treatments using an AFT model, and then estimated the treatment effect in terms of a HR. We then fitted an AFT model to the control group, and estimated survival in the experimental group using the estimated HR. We compared the restricted mean survival time (RMST) estimated for the experimental group to the true RMST. Mean percentage bias was estimated over 1,000 iterations. The study explored whether the scale of bias varied depending on the AFT model, the size of the treatment effect or whether censoring was present.

RESULTS: The percentage bias in estimates of experimental group RMST varied significantly depending on the AFT model and the size of the treatment effect. When the survival data followed a Weibull distribution, estimates were not biased. When the survival data followed log-normal or log-logistic distributions, bias ranged from negligible with a treatment effect of one, up to 87% with a HR of 0.5.

CONCLUSIONS: The application of a HR to an AFT model can cause biased survival estimates. Bias is greater when log-normal or log-logistic models are used, and when the treatment effect is large.